Why is the assigned material larger than the selected faces?
You experiencing this problem because of the Subdivision-Surface modifier.
When you add in a default sub-surf modifier, it just displays the modifier in the edit mode (as well as in the object mode) but won't show the change in geometry that the sub-surf modifier makes. Here is an example with respect to your model:

Notice how the geometry change when the subdivision surface is switched on.
To solve your problem just make Loop cuts with Edit Cage on.(the icon in the circle):